Subgroups — C₇×#21339 #13198555

Order 1792.

814 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₇×#1984	C₂	1	2	yes	maximal
3	C₇×#1939	C₂	1	2	yes	maximal
4	C₇×#1916	C₂	1	4	yes	maximal
5	C₄×C₇×C₄⋊C₈	C₂	1	2	yes	maximal
6	C₄×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₇×#1744	C₂	1	2	yes	maximal
8	C₄²×C₇×C₈	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₇×Q₈	C₄	1	1	yes	characteristic
10	C₂×C₄×C₇×Q₈	C₄	1	1	yes	characteristic
11	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	—
14	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
16	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
18	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
19	C₄×C₇×C₄⋊C₄	C₄	1	2	yes	—
20	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₇×C₄⋊C₄	C₄	1	2	yes	—
22	C₄×C₇×C₄⋊C₄	C₄	1	1	yes	characteristic
23	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
24	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₄³×C₇	C₂²	1	1	yes	characteristic
26	C₄³×C₇	C₂²	1	2	yes	—
27	C₇×#336	C₂²	1	4	yes	—
28	C₇×#336	C₂²	1	4	yes	—
29	C₇×#336	C₂²	1	4	yes	—
30	C₇×#336	C₂²	1	2	yes	—
31	#21339	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₇×C₈	C₂³	1	4	yes	—
34	C₂²×C₇×C₈	C₂³	1	2	yes	—
35	C₂²×C₇×C₈	C₂³	1	2	yes	—
36	C₄×C₇×Q₈	—	2	4	no	—
37	C₄×C₇×Q₈	—	2	4	no	—
38	C₄×C₇×Q₈	C₈	1	8	yes	complemented
39	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
40	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
41	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
44	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₇	C₂³	1	2	yes	—
54	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₇	C₂³	1	2	yes	—
56	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
58	C₇×C₄⋊C₈	—	2	8	no	—
59	C₇×C₄⋊C₈	—	2	4	no	—
60	C₄×C₇×C₈	—	2	4	no	—
61	C₄×C₇×C₈	—	2	4	no	—
62	C₄×C₇×C₈	—	2	2	no	—
63	C₄×C₇×C₈	—	2	4	no	—
64	C₄×C₇×C₈	Q₈	1	4	yes	complemented
65	C₇×#95	C₂×C₄	1	2	yes	—
66	C₇×#95	C₂×C₄	1	2	yes	—
67	C₇×#95	C₂×C₄	1	2	yes	—
68	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic
69	#1984	C₂×C₇	1	2	yes	—
70	#1939	C₂×C₇	1	2	yes	—
71	#1916	C₂×C₇	1	4	yes	—
72	C₄×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic
73	C₄×C₄⋊C₈	C₂×C₇	1	2	yes	—
74	#1744	C₂×C₇	1	2	yes	—
75	C₄²×C₈	C₂×C₇	1	1	yes	characteristic
76	C₂×C₇×Q₈	—	2	2	no	—
77	C₂×C₇×Q₈	—	2	2	no	—
78	C₂×C₇×Q₈	C₂×C₈	1	4	yes	—
79	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
90	C₂×C₇×C₈	—	2	2	no	—
91	C₂×C₇×C₈	—	2	2	no	—
92	C₂×C₇×C₈	—	2	2	no	—
93	C₂×C₇×C₈	—	2	2	no	—
94	C₂×C₇×C₈	—	2	4	no	—
95	C₂×C₇×C₈	—	2	4	no	—
96	C₂×C₇×C₈	—	2	4	no	—
97	C₂×C₇×C₈	C₂×Q₈	1	4	yes	—
98	C₂×C₇×C₈	#41	1	4	yes	—
99	C₇×C₄⋊C₄	—	2	4	no	—
100	C₇×C₄⋊C₄	—	2	2	no	—
101	C₇×C₄⋊C₄	—	2	4	no	—
102	C₇×C₄⋊C₄	—	2	2	no	—
103	C₇×C₄⋊C₄	C₂×C₈	1	8	yes	—
104	C₇×C₄⋊C₄	C₂×C₈	1	4	yes	—
105	C₄²×C₇	—	2	4	no	—
106	C₄²×C₇	—	2	2	no	—
107	C₄²×C₇	—	2	2	no	—
108	C₄²×C₇	—	2	4	no	—
109	C₄²×C₇	—	2	4	no	—
110	C₄²×C₇	—	2	2	no	—
111	C₄²×C₇	—	2	4	no	—
112	C₄²×C₇	—	2	4	no	—
113	C₄²×C₇	C₂×C₈	1	8	yes	—
114	C₄²×C₇	C₂×C₈	1	4	yes	—
115	C₄²×C₇	M₁₆	1	4	yes	—
116	C₄²×C₇	C₂×Q₈	1	2	yes	—
117	C₄²×C₇	#41	1	4	yes	—
118	C₄²×C₇	#41	1	2	yes	—
119	C₂×C₄×Q₈	C₄×C₇	1	1	yes	characteristic
120	C₂×C₄×Q₈	C₄×C₇	1	1	yes	characteristic
121	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
122	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	—
123	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
124	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
125	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
126	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
127	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
128	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
129	C₄×C₄⋊C₄	C₄×C₇	1	2	yes	—
130	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
131	C₄×C₄⋊C₄	C₄×C₇	1	2	yes	—
132	C₄×C₄⋊C₄	C₄×C₇	1	1	yes	characteristic
133	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
134	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
135	C₄³	C₂²×C₇	1	1	yes	characteristic
136	C₄³	C₂²×C₇	1	2	yes	—
137	#336	C₂²×C₇	1	2	yes	—
138	#336	C₂²×C₇	1	4	yes	—
139	#336	C₂²×C₇	1	4	yes	—
140	#336	C₂²×C₇	1	4	yes	—
141	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
142	C₇×Q₈	—	2	8	no	—
143	C₂×C₄×C₇	—	2	2	no	—
144	C₂×C₄×C₇	—	2	1	no	—
145	C₂×C₄×C₇	—	2	2	no	—
146	C₂×C₄×C₇	—	2	1	no	—
147	C₂×C₄×C₇	—	2	2	no	—
148	C₂×C₄×C₇	—	2	1	no	—
149	C₂×C₄×C₇	—	2	1	no	—
150	C₂×C₄×C₇	—	2	1	no	—
151	C₂×C₄×C₇	—	2	2	no	—
152	C₂×C₄×C₇	—	2	1	no	—
153	C₂×C₄×C₇	—	2	2	no	—
154	C₂×C₄×C₇	—	2	2	no	—
155	C₂×C₄×C₇	—	2	2	no	—
156	C₂×C₄×C₇	—	2	2	no	—
157	C₂×C₄×C₇	—	2	2	no	—
158	C₂×C₄×C₇	—	2	2	no	—
159	C₂×C₄×C₇	#117	1	2	yes	—
160	C₂×C₄×C₇	#117	1	2	yes	—
161	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
162	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
163	C₂×C₄×C₇	C₂²×C₈	1	4	yes	—
164	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
165	C₂×C₄×C₇	C₂²×C₈	1	4	yes	—
166	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
167	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
168	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
169	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
171	C₂×C₄×C₇	#131	1	2	yes	—
172	C₂×C₄×C₇	#131	1	2	yes	—
173	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₇	C₂×#41	1	2	yes	—
176	C₂×C₄×C₇	C₂×#41	1	2	yes	—
177	C₇×C₈	—	2	4	no	—
178	C₇×C₈	—	2	4	no	—
179	C₇×C₈	—	4	4	no	—
180	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
181	C₂²×C₈	C₂³×C₇	1	4	yes	—
182	C₂²×C₈	C₂³×C₇	1	2	yes	—
183	C₂²×C₈	C₂³×C₇	1	2	yes	—
184	C₄×Q₈	—	2	4	no	—
185	C₄×Q₈	—	2	4	no	—
186	C₄×Q₈	C₇×C₈	1	8	yes	complemented
187	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
188	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
189	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
190	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
191	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
192	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
193	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
194	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
195	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
196	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
197	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
198	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
199	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
200	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
201	C₂×C₄²	C₂³×C₇	1	2	yes	—
202	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
203	C₂×C₄²	C₂³×C₇	1	2	yes	—
204	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
205	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
206	C₄⋊C₈	—	2	8	no	—
207	C₄⋊C₈	—	2	4	no	—
208	C₄×C₈	—	2	4	no	—
209	C₄×C₈	—	2	4	no	—
210	C₄×C₈	—	2	2	no	—
211	C₄×C₈	—	2	4	no	—
212	C₄×C₈	C₇×Q₈	1	4	yes	complemented
213	#95	C₂×C₄×C₇	1	2	yes	—
214	#95	C₂×C₄×C₇	1	2	yes	—
215	#95	C₂×C₄×C₇	1	2	yes	—
216	C₂²×C₇	C₂×#117	1	1	yes	characteristic
217	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
218	C₂²×C₇	C₄×#41	1	1	yes	characteristic
219	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
220	C₂²×C₇	C₂²×M₁₆	1	1	yes	characteristic
221	C₂²×C₇	C₂×#131	1	1	yes	characteristic
222	C₂²×C₇	C₂×#131	1	1	yes	characteristic
223	C₄×C₇	—	2	4	no	—
224	C₄×C₇	—	2	2	no	—
225	C₄×C₇	—	2	2	no	—
226	C₄×C₇	—	2	4	no	—
227	C₄×C₇	—	2	2	no	—
228	C₄×C₇	—	4	2	no	—
229	C₄×C₇	—	4	2	no	—
230	C₄×C₇	#431	1	4	yes	—
231	C₄×C₇	C₈×Q₈	1	4	yes	—
232	C₄×C₇	#446	1	4	yes	—
233	C₄×C₇	#529	1	2	yes	—
234	C₄×C₇	#533	1	2	yes	—
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	—	2	2	no	—
237	C₂×Q₈	C₂×C₇×C₈	1	4	yes	—
238	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
239	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
240	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
243	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
244	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
246	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
247	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
248	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	C₂×C₇×Q₈	1	4	yes	—
257	C₂×C₈	C₇×#41	1	4	yes	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	—	2	2	no	—
260	C₄⋊C₄	—	2	4	no	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	C₂×C₇×C₈	1	8	yes	—
263	C₄⋊C₄	C₂×C₇×C₈	1	4	yes	—
264	C₄²	—	2	4	no	—
265	C₄²	—	2	2	no	—
266	C₄²	—	2	2	no	—
267	C₄²	—	2	4	no	—
268	C₄²	—	2	4	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	4	no	—
271	C₄²	—	2	4	no	—
272	C₄²	C₂×C₇×C₈	1	8	yes	—
273	C₄²	C₂×C₇×C₈	1	4	yes	—
274	C₄²	C₇×M₁₆	1	4	yes	—
275	C₄²	C₂×C₇×Q₈	1	2	yes	—
276	C₄²	C₇×#41	1	4	yes	—
277	C₄²	C₇×#41	1	2	yes	—
278	C₂×C₇	#2295	1	1	yes	characteristic
279	C₂×C₇	C₂×#431	1	1	yes	characteristic
280	C₂×C₇	#2922	1	1	yes	characteristic
281	C₂×C₇	C₂×C₈×Q₈	1	1	yes	characteristic
282	C₂×C₇	C₂×#446	1	1	yes	characteristic
283	C₂×C₇	C₈×#41	1	1	yes	characteristic
284	C₂×C₇	#2965	1	1	yes	characteristic
285	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
286	Q₈	—	2	8	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	C₇×#117	1	2	yes	—
304	C₂×C₄	C₇×#117	1	2	yes	—
305	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
306	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
307	C₂×C₄	C₂²×C₇×C₈	1	4	yes	—
308	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
309	C₂×C₄	C₂²×C₇×C₈	1	4	yes	—
310	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
311	C₂×C₄	C₂²×C₇×C₈	1	2	yes	—
312	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
313	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
314	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
315	C₂×C₄	C₇×#131	1	2	yes	—
316	C₂×C₄	C₇×#131	1	2	yes	—
317	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
318	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
319	C₂×C₄	C₂×C₇×#41	1	2	yes	—
320	C₂×C₄	C₂×C₇×#41	1	2	yes	—
321	C₈	—	2	4	no	—
322	C₈	—	2	4	no	—
323	C₈	—	4	4	no	—
324	C₇	#21339	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²	C₂×C₇×#117	1	1	yes	characteristic
326	C₂²	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
327	C₂²	C₄×C₇×#41	1	1	yes	characteristic
328	C₂²	C₂³×C₇×C₈	1	1	yes	characteristic
329	C₂²	C₂²×C₇×M₁₆	1	1	yes	characteristic
330	C₂²	C₂×C₇×#131	1	1	yes	characteristic
331	C₂²	C₂×C₇×#131	1	1	yes	characteristic
332	C₄	—	2	4	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	4	no	—
336	C₄	—	2	2	no	—
337	C₄	—	4	2	no	—
338	C₄	—	4	2	no	—
339	C₄	C₇×#431	1	4	yes	—
340	C₄	C₇×C₈×Q₈	1	4	yes	—
341	C₄	C₇×#446	1	4	yes	—
342	C₄	C₇×#529	1	2	yes	—
343	C₄	C₇×#533	1	2	yes	—
344	C₂	C₇×#2295	1	1	yes	characteristic
345	C₂	C₂×C₇×#431	1	1	yes	characteristic
346	C₂	C₇×#2922	1	1	yes	characteristic
347	C₂	C₂×C₇×C₈×Q₈	1	1	yes	characteristic
348	C₂	C₂×C₇×#446	1	1	yes	characteristic
349	C₂	C₇×C₈×#41	1	1	yes	characteristic
350	C₂	C₇×#2965	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₇	C₂³
commutator	C₂²	C₂³×C₇×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle, prime radical	C₂³×C₇	C₂³×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
31. #21339	C₇	direct (N × H)
38. C₄×C₇×Q₈	C₈	semidirect
64. C₄×C₇×C₈	Q₈	semidirect
186. C₄×Q₈	C₇×C₈	semidirect
212. C₄×C₈	C₇×Q₈	semidirect
324. C₇	#21339	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄²×C₇×Q₈	2
C₇×#1984	2
C₇×#1939	2
C₇×#1916	2
C₄×C₇×C₄⋊C₈	2
C₇×#1744	2
C₄²×C₇×C₈	2
#21339	7

Subgroups — C7×#21339 #13198555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21339 #13198555